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University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
290
Compressibilty of Soils
H
Deformation of soil grains
Expulsion of water
Relocation of soil particles
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
291
Topics Introduction Immediate Settlement Consolidation Settlement (Primary Consolidation) Secondary Compression (Secondary consolidation)
Settlement Time Rate of Consolidation Methods for Accelerating Consolidation Settlement
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
160
Introduction Soil deformation may occur by change in:
a) Stress b) Water content c) Soil mass d) Temperature
The compression is caused by a) Deformation of soil particles b) Relocation of soil particles c) Expulsion of water or air from the voids
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
161
Types of settlement: a) Immediate (Elastic) Settlement e b) Consolidation Settlement (primary consolidation) c c) Secondary Compression (Consolidation) Settlement s Thus, the total settlement will be sceT
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
162
Immediate (Elastic) Settlement Due elastic deformation of soil grains without any change in moisture content It is usually small and occurs directly after the application of a load. The magnitude of the contact settlement will depend on the flexibility of the foundation and the type of material on which it is resting, these distributions are true if E is constant with depth.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
163
all the previous relationship discussed in previous chapter were based on the following assumptions:-
a) The load is applied at the ground surface
Flexible
Rigid
Sand Clay Contact pressure distribution
Contact pressure distribution
Contact pressure distribution
Contact pressure distribution
Settlement profile Settlement profile
Settlement profile Settlement profile
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
164
b) The loaded area is flexible. c) The soil medium is homogenous, elastic, isotropic,
and extends to a great depth. Relations for Immediate Settlement Calculation
ps
se I
EB
21
Schleicher (1926)
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
165
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
166
Improved Relationship for Immediate Settlement Mayne and Polous (1999) present an improved relationship for calculating e taking into account –
- rigidity of the foundation - depth of embedment of the foundation - the increase in modulus of elasticity E with depth - the location of rigid layers at limited depth
EFGo
see III
EB
21
BLBe4
for rectangular footing
DiameterBe for circular footing
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
167
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
168
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
169
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
170
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
171
Consolidation Settlement (Primary Consolidation) Fundamentals of Consolidation Deformation of saturated soil occurs by reduction of pore space & the squeezing out of pore water. The water can only escape through the pores which for fine-grained soils are very small, while for coarse-grained soils are large enough for the process to occur immediately after the application of load.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
172
Skeletal Material (incompressible)
Pore water (Incompressible)
Voids
Solid
Voids
Solid
Initial State Deformed State
Water
+
Time dependent
process
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
173
Spring model
water
Effective soil skeleton “spring”
Water squeezed out
u
P = P/A
u < u = 0 u = 0
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
174
Total Stress
Time
Time
Excess Pore Pressure
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
175
Effective Stress
Time
Settlement
Time
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
176
Conclusions Especially in low permeability soils (silts and clays) settlement is delayed by the need to squeeze the water out of the soil
Consolidation is the process of gradual transfer of an applied load from the pore water to the soil structure as pore water is squeezed out of the voids.
The amount of water that escapes depends on the size of the load and compressibility of the soil.
The rate at which it escapes depends on the coefficient of permeability, thickness, and compressibility of the soil.
Consider a clay layer with thickness H subjected to an instantaneous increase of total stress .
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
177
Ground water table
Total stress increase Pore water pressure increase Effective stress increase
At time t = 0
At time 0 < t <
At time t =
u = / = 0 H
Depth Sand
Sand
u = 0 / =
/ > 0 u <
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
178
One-Dimensional Laboratory Consolidation Test It was suggested by Terzaghi.
Consolidometer (Oedometer)
pn applied by a lever arm
H
Porous Stone
Porous Stone
Soil Sample
Dia. 64 mm(2.5 in)
H 25 mm (1 in)
Metal Ring Sample
Water
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
179
p1 p2 p3 pn
H
H1 H2 H3 Hn
Each load increment is kept for 24 hrs, after that, the load is usually doubled
The compression deformation is measured by a micrometer dial gauge
h
hn
Settlement (deformation) vs. time
U% = 100% Time at U%=100%
t50%
U% = 0
H d50
d100
d0 Stage I-Initial compression
Stage II-Primary consolidation
Stage III-Secondary Compression
Time (log scale)
Soil
Time, min Deformation, mm o
¼ ½ 1 2 5 10 20 30 1 hr 2 hr …….. 24 hr
Cv & k are determined from this relationship
At each time point: Record the dial indicator reading At the end of each load increment: Record the dial reading at completion of primary consolidation for each load (usually 24 hours) At the unloading of the specimen: Remove load in decrements, recording dial indicator readings Conduct a water content test on specimen after unloading is complete
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
180
Void Ratio-Pressure (e-log 1. calculate the height of solids, Hs
ws
ss AG
WH Prove it.
2. calculate initial height of voids, Hv sHHH
3. calculate initial void ratio, eo
s
v
s
v
v
vo H
HAHAH
VVe
4. for the 1st incremental loading, 1 ( AP1 ) which causes a
deformation H1
sHHe 1
1
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
181
5. calculate new void ratio after consolidation caused by 1 11 eee o
6. for the next loading, 2 ( APP 21 ), which causes additional
deformation H2, the void ratio at the end of consolidation is
sHHee 2
12
Note:- at the end of consolidation = / Plot the corresponding e with / on semi-logarithmic paper. The typical shape of e-log / will be as shown in the figure.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
182
Change in void ratio vs. vertical effective stress
Void Ratio
Log /
Cc & Cs are determined from this relationship
Cc = Compression Index
Cs (Cr) = swelling (rebound) Index
Cc
Cs
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
183
Normally Consolidated and Overconsolidated Clays
O
PRCO ..
Log / /
O /P
At past
p = max. preconsolidation pressure
At past
p = max. preconsolidation pressure
At present
o = Effective overburden pressure
At present
o = Effective overburden pressure
Normally Consolidated
Overconsolidated
po
po
May be removed due geologic processes or human processes
Relationship is linear and stepper when the effective stresses is exceeding maximum past preconsolidation pressure
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
184
Effect of Disturbance on Void Ratio-Pressure Relationship
Usually e-log / founded by performing consolidation test on undisturbed sample or remolded sample, does not reflects the field (virgin) compression curve.
This difference is attribute to disturbance due to-
Handling and transferring samples into consolidation cells. Sampling and stress relief
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
185
0.4eo
0.4eo
Laboratory compression curve
Field (virgin) compression curve, Slope = Cc
Laboratory rebound curve Slope = Cs (Cr)
p/ = o
/
Laboratory compression curve eo
Field (virgin) compression curve
Slope = Cc
eo
p/
o/
N.C. CLAY
O.C. CLAY
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
186
Calculation of Settlement from One-Dimensional Primary Consolidation
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
187
oc
osc
oo
os
svvvo
cco
eeH
eAHeeVAV
eAH
eVV
eVVVVVAAHHAVVV
1
1
11
)(
1
1
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
188
N.C. CLAY
O.C. CLAY
)log(11
)log(]log)[log(log
o
o
o
c
oc
o
ocoocc
He
CeeH
CCeeC
eo
p/
o/
p/ = o
/ o/ + /
eo
e
eo
p/
o/
o/ + /
)log(11
log(]log)[log(log
o
o
o
s
oc
o
osooss
He
CeeH
CCeeC
If o/ + / /
p
If o/ + / /
p
)log()log(11
)log()log(
]log)[log(]log[log21
p
oc
o
ps
ooc
p
oc
o
ps
pocops
CCe
HeeH
CC
CCeee
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
189
Compression Index (Cc) and Swell Index (Cs) Several correlations were suggested for Cc besides other eq. and in most cases cs CtoC
101
51
Cc = 0.009(LL – 10) undisturbed clays LL= liquid limit Cc = 0.007(LL – 7) remolded clays LL= liquid limit =
o/ + /
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
190
Secondary Compression (Consolidation) Settlement Secondary compression settlement is a form of soil creep that is largely controlled by the rate at which the skeleton of compressible soils, particularly clays, silts, and peats, can yield and compress. Secondary compression is often conveniently identified to follow primary consolidation when excess pore fluid pressure can no longer be measured; however, both processes may occur simultaneously. Also referred to as the “secular effect”
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
191
1
212 logloglogtt
ett
eC
peCC
1
1
2logttHCs
Type of soil C O.C clays 0.001 or less N.C clays 0.005 to 0.03 Organic soil 0.04 or more
Linear relationship
e
t1 t2
ef
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
192
Time Rate of Consolidation Terzaghi (1925) proposed the first theory to consider the rate of one-dimensional consolidation for saturated clay soils.
Assumptions:-
1. The clay-water system is homogenous. 2. Saturation is complete. 3. Compressibility of water is negligible 4. The flow of water is in one direction only (direction of
compression) 5. Darcy’s law is valid
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
193
To begin, consider a very small element of soil being subjected to one-dimensional consolidation in the z-direction.
H=2Hdr
Depth Sand
Sand
w
uh
vz dxdy
A=dxdy
V=dxdydz
dx dy
dz
(vz+( vz z)dz) dxdy
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
194
Volume of pore fluid which flows out = Volume decrease of the soil
and thus Rate at which pore fluid flows out = Rate of volume decrease of
soil
tVdxdydz
zv
tVdxdyvdz
zv
v
z
zz
z ])[(
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
195
It will also be assumed that Darcy’s law holds and thus that
zuk
zhkkiv
wz
w
uh u = excess pore water pressure caused by the increase of stress
tV
dxdydzzuk
w
12
2
During consolidation
tVe
teV
tV
teVV
tV
tV s
ssssv )(
but 0t
Vs
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
196
teV
tV
s but oo
s edxdydz
eVV
11
te
edxdydz
tV
o1
te
ezuk
ow 11
2
2
But uaae vv )( av = coefficient of compressibility
tum
tu
ea
zuk
vo
v
w 12
2
where o
vv e
am1
mv = coefficient of volume compressibility
/
e
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
197
or 2
2
zuc
tu
v where o
vw
vwv
ea
kmkc
1
cv = coefficient of consolidation has units L2/T k = coefficient of permeability This equation is the basic differential equation of Terzaghi,s consolidation theory and can be solved with the following boundary conditions
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
198
z = 0 u = 0 at a permeable boundary z = 2Hdr u = 0 at a permeable boundary t = 0 u = uo= initial excess pore water pressure The solutions yields
vTM
m dr
o eHMZ
Muu
2
0)(sin2
Where
)12(2
mM
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
199
drHzZ , a depth factor dimensionless number
2dr
vv H
tcT , a time factor is a nondimensoinal number
Because consolidation progresses by the dissipation of excess pore water pressure, the degree of consolidation at distance z at any time t is
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
200
o
z
o
zoz u
uu
uuU 1
uz = excess pore pressure at time t The variation of excess pore pressure within the layer is shown in Figure below
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
201
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
202
The average degree of consolidation for the entire depth of the clay layer at any time t can be written as
m
m
TM
o
H
zdr
c
tc v
dr
eMu
dzuH
U0
2
2
0)( 221
21
1 U = average degree of consolidation
c(t) = settlement of the layer at time t c = ultimate (final) primary consolidation settlement
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
203
The U – Tv relationship is represented in the figure below for the case where uo is uniform for the entire depth of the consolidating layer.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
204
The values of Tv and their corresponding average U for the case presented above may also be approximately by the following relationship:
For U = 0 to 60% 2
100%
4UTv
For U > 60% %)100log(933.0781.1 UTv The following Table gives the variation Tv – U according to the above equations
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
205
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
206
Coefficient of Consolidation
Logarithm of Time method It is particularly useful when there is significant secondary compression (creep). The do point is located by selected two points on the curve for which the times (t) are in the ratio 1:4, e.g. 1 min and 4 min; or 2 min and 8 min.; the vertical intervals DB and BC will be equal. The d100 point can be located in the final part of the curve flattens sufficiently (i.e. no secondary compression). When there is significant secondary compression, d100 may be located at the intercept of straight line drawn through the middle and final portions of the curve. Now d50 and log t50 can be located.
The coefficient of consolidation is therefore:
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
207
50
2
250
50197.0
tHc
HtcT dr
vdr
v
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
208
Square Root of Time method After the laboratory results curve has been plotted, line AB is drawn, followed by line AC in such a way that OBOC 15.1 : AC crosses the laboratory curve at point D and locates 90t
The coefficient of consolidation is therefore:
90
2
290
90848.0
tH
cH
tcT dr
vdr
v
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
209
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
210
Hperbola method It gives good results for U =60% - 90%.
The results are plotted on Ht
- t, then identify the straight portion bc of the curve and project back to point d, and determine the intercept D, then determine the slope m of bc
The coefficient of consolidation is therefore: DmHc dr
v
2
3.0
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
211
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
212
Earl Stage log-t method It gives the highest value while the conventional log-t method gives the lowest value, this is due to the contribution of the lower part of the consolidation curve in the conventional log-t method that means the secondary compression plays a role in the value of cv, while in this method cv obtained from the early stage log-t method, which gives more realistic values of the fieldwork. Follow the same steps in log-t method to locate do, draw a horizontal line DE through do, then draw tangent through the point of inflection F, the tangent intersects line DE at point G, determine the corresponding time t corresponding to G, which is the time at U = 22.14%, The coefficient of consolidation is therefore:
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
213
14.22
20385.0t
Hc drv
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
214
Calculation of Consolidation Settlement under a Foundation For limited area foundations (circular, square and rectangular), the increase of effective stress ( /) decrease with depth as shown in figure below which can be estimated as described before in previous chapter.
Estimate /o and /
av at the middle of the clay layer, then use the previous equations in to determine final consolidation settlement.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
215
Using Simpson’s rule
64 bmt
av
/o /
m
/b
/t
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
216
Alternative approach Simply divide the clay layer to a number of sub layers, and then estimate c for each sub layer taking into account effective overburden pressure and an increase in effective stress at the middle of each sub layer, then get the summation of settlements of the sub layers to get the final consolidation of the clay layer.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
217
Rate of consolidation It is important to determine c – time relationship, which can be helpful in estimating the differential settlement between adjacent footings if the drainage condition at one footing differs from the other.
c
tcU )(
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
218
Examples The following results were obtained from an oedometer test on a specimen of saturated clay: Pressure (kN/m2) 27 54 107 214 429 214 107 54 Void ratio 1.243 1.217 1.144 1.068 0.994 1.001 1.012 1.024 A layer of this clay 8m thick lies below a 4m depth of sand, the water table being at the surface. The saturated unit weight for both soils is 19kN/m3. A 4m depth of fill of unit weight 21 kN/m3 is placed on the sand over an extensive area. Determine the final settlement due to consolidation of the clay. If the fill were to be removed some time after the completion of
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
219
consolidation, what heave would eventually take place due to swelling of the clay?
Heeeo
oc 1
1
Appropriate values of e are obtained from e-log / drawn from the result. The clay will be divided into four sub-layers, hence H =2000 mm.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
220
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
221
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
222
Assuming the fill in pervious example is dumped very rapidly, what would be the value of excess pore water pressure at the centre of the clay layer after a period of 3 years? Assume Two-way drainage condition and the value of cv is 2.4m2/year.
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
223
2/2.35
58.084
1
mkNu
uu
uuU
z
z
o
zoz
University of Anbar College of Engineering Civil Engineering Department Iraq-Ramadi
Asst. Prof. Khalid R. Mahmood (PhD.)
224
In an oedometer test a specimen of saturated clay 19mm thick reaches 50% consolidation in 20 min. How long would it take a layer of this clay 5m thick to reach the same degree of consolidation under the same stress and drainage conditions? How long would it take the layer to reach 30% consolidation?
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